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Weyl functions and the Ap condition on compact lie groups

Part of: Abstract harmonic analysis

Published online by Cambridge University Press:  09 April 2009

Giancarlo Travaglini
Giancarlo Travaglini
Affiliation:
Istituto Matematico dell'UniversitàVia Saldini 50 20133 Milano, Italy
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Abstract

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Let G be a compact, simple, simply connected Lie group. The Lp-norm of a central trigonometric polynomial reduces naturally to a weighted Lp-norm of a trigonometric polynomial on a maximal torus T. The weight is | Δ |2-p, where Δ is the usual Weyl function. If p ≥ 2, we prove that | Δ |2-p satisfies Muckenhoupt's Ap condition if and only if the Lp-norms of the irreducible characters of G are uniformly bounded.

MSC classification

Secondary: 43A15: $L^p$-spaces and other function spaces on groups, semigroups, etc. 43A40: Character groups and dual objects
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 33 , Issue 2 , October 1982 , pp. 185 - 192
Copyright
Copyright © Australian Mathematical Society 1982

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